First-Principles Calculation of ortho–para Effects in the Second Virial Coefficients of H2 and D2 at Low Temperatures

We report ab initio calculations of the second virial coefficient B(T) of molecular hydrogen isotopologues in the rigid-rotor approximation using the path-integral Monte Carlo method. We present a novel method for efficient sampling of rotational degrees of freedom based on Doob’s h-transform that can be used with any spin isomer, including those for which the quantum mechanical propagator in imaginary time is negative, e.g., ortho-H2. Additionally, we extend the theory to evaluate the contribution to B(T) due to quantum statistical effects, relevant at low temperatures. This allows us to compute the difference in B(T) between para-H2 and normal H2; our calculation of this difference near 20 K is in qualitative agreement with the only available experimental measurements.